itkHexahedronCell.txx

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/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkHexahedronCell.txx,v $
  Language:  C++
  Date:      $Date: 2008-10-17 01:21:45 $
  Version:   $Revision: 1.38 $

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/
#ifndef __itkHexahedronCell_txx
#define __itkHexahedronCell_txx
#include "itkHexahedronCell.h"
#include "vnl/vnl_matrix_fixed.h"
#include "vnl/algo/vnl_determinant.h"

namespace itk
{

template <typename TCellInterface >
void
HexahedronCell< TCellInterface >
::MakeCopy(CellAutoPointer & cellPointer) const
{
  cellPointer.TakeOwnership( new Self );
  cellPointer->SetPointIds(this->GetPointIds());
}

template <typename TCellInterface>
unsigned int
HexahedronCell< TCellInterface >
::GetDimension(void) const
{
  return Self::CellDimension;
}

template <typename TCellInterface>
unsigned int
HexahedronCell< TCellInterface >
::GetNumberOfPoints(void) const
{
  return Self::NumberOfPoints;
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::CellFeatureCount
HexahedronCell< TCellInterface >
::GetNumberOfBoundaryFeatures(int dimension) const
{
  switch (dimension)
    {
    case 0: return GetNumberOfVertices();
    case 1: return GetNumberOfEdges();
    case 2: return GetNumberOfFaces();
    default: return 0;
    }
}

template <typename TCellInterface>
bool
HexahedronCell< TCellInterface >
::GetBoundaryFeature(int dimension, CellFeatureIdentifier featureId,
                     CellAutoPointer & cellPointer )
{
  switch (dimension)
    {
    case 0:
      {
      VertexAutoPointer vertexPointer;
      if( this->GetVertex(featureId,vertexPointer) )
        {
        TransferAutoPointer(cellPointer,vertexPointer);
        return true;
        }
      else
        {
        cellPointer.Reset();
        return false;
        }
      break;
      }
    case 1:
      {
      EdgeAutoPointer edgePointer;
      if( this->GetEdge(featureId,edgePointer) )
        {
        TransferAutoPointer(cellPointer,edgePointer);
        return true;
        }
      else
        {
        cellPointer.Reset();
        return false;
        }
      break;
      }
    case 2:
      {
      FaceAutoPointer facePointer;
      if( this->GetFace(featureId,facePointer) )
        {
        TransferAutoPointer(cellPointer,facePointer);
        return true;
        }
      else
        {
        cellPointer.Reset();
        return false;
        }
      break;
      }
    default:
      {
      cellPointer.Reset();
      return false;
      }
    }
  return false;
}

template <typename TCellInterface>
void
HexahedronCell< TCellInterface >
::SetPointIds(PointIdConstIterator first)
{
  PointIdConstIterator ii(first);
  for( int i=0; i < Self::NumberOfPoints; ++i )
    {
    m_PointIds[i] = *ii++;
    }
}

template <typename TCellInterface>
void
HexahedronCell< TCellInterface >
::SetPointIds(PointIdConstIterator first, PointIdConstIterator last)
{
  int localId=0;
  PointIdConstIterator ii(first);

  while(ii != last)
    {
    m_PointIds[localId++] = *ii++;
    }
}

template <typename TCellInterface>
void
HexahedronCell< TCellInterface >
::SetPointId(int localId, PointIdentifier ptId)
{
  m_PointIds[localId] = ptId;
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::PointIdIterator
HexahedronCell< TCellInterface >
::PointIdsBegin(void)
{
  return &m_PointIds[0];
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::PointIdConstIterator
HexahedronCell< TCellInterface >
::PointIdsBegin(void) const
{
  return &m_PointIds[0];
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::PointIdIterator
HexahedronCell< TCellInterface >
::PointIdsEnd(void)
{
  return &m_PointIds[Self::NumberOfPoints-1] + 1;
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::PointIdConstIterator
HexahedronCell< TCellInterface >
::PointIdsEnd(void) const
{
  return &m_PointIds[Self::NumberOfPoints-1] + 1;
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::CellFeatureCount
HexahedronCell< TCellInterface >
::GetNumberOfVertices(void) const
{
  return Self::NumberOfVertices;
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::CellFeatureCount
HexahedronCell< TCellInterface >
::GetNumberOfEdges(void) const
{
  return Self::NumberOfEdges;
}

template <typename TCellInterface>
typename HexahedronCell< TCellInterface >::CellFeatureCount
HexahedronCell< TCellInterface >
::GetNumberOfFaces(void) const
{
  return Self::NumberOfFaces;
}

template <typename TCellInterface>
bool
HexahedronCell< TCellInterface >
::GetVertex(CellFeatureIdentifier vertexId,VertexAutoPointer & vertexPointer )
{
  VertexType * vert = new VertexType;
  vert->SetPointId(0, m_PointIds[vertexId]);
  vertexPointer.TakeOwnership( vert );
  return true;
}

template <typename TCellInterface>
bool
HexahedronCell< TCellInterface >
::GetEdge(CellFeatureIdentifier edgeId, EdgeAutoPointer & edgePointer )
{
  EdgeType * edge = new EdgeType;
  for(int i=0; i < EdgeType::NumberOfPoints; ++i)
    {
    edge->SetPointId(i, m_PointIds[ m_Edges[edgeId][i] ]);
    }
  edgePointer.TakeOwnership( edge );
  return true;
}


template <typename TCellInterface>
bool
HexahedronCell< TCellInterface >
::GetFace(CellFeatureIdentifier faceId, FaceAutoPointer & facePointer )
{
  FaceType * face = new FaceType;
  for(unsigned int i=0; i < FaceType::NumberOfPoints; ++i)
    {
    face->SetPointId(i, m_PointIds[ m_Faces[faceId][i] ]);
    }
  facePointer.TakeOwnership( face );
  return true;
}

template <typename TCellInterface>
bool
HexahedronCell< TCellInterface >
::EvaluatePosition(CoordRepType* x,
                   PointsContainer* points,
                   CoordRepType* closestPoint,
                   CoordRepType pcoord[3],
                   double* dist2,
                   InterpolationWeightType* weight)
{
  static const int ITK_HEX_MAX_ITERATION=10;
  static const double ITK_HEX_CONVERGED=1.e-03;
  static const double ITK_DIVERGED = 1.e6;

  int iteration, converged;
  double  params[3];
  double  fcol[3], rcol[3], scol[3], tcol[3];
  double  d;
  PointType pt;
  CoordRepType derivs[24];
  InterpolationWeightType weights[8];

  //  set initial position for Newton's method
  int subId = 0;
  CoordRepType pcoords[3];
  pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2]=0.5;

  //  enter iteration loop
  for (iteration=converged=0;
       !converged && (iteration < ITK_HEX_MAX_ITERATION);  iteration++)
    {
    //  calculate element interpolation functions and derivatives
    this->InterpolationFunctions(pcoords, weights);
    this->InterpolationDerivs(pcoords, derivs);

    //  calculate newton functions
    for (unsigned int i=0; i<3; i++)
      {
      fcol[i] = rcol[i] = scol[i] = tcol[i] = 0.0;
      }
    for (unsigned int i=0; i<8; i++)
      {
      pt = points->GetElement( m_PointIds[i] );
      for (unsigned int j=0; j<3; j++)
        {
        fcol[j] += pt[j] * weights[i];
        rcol[j] += pt[j] * derivs[i];
        scol[j] += pt[j] * derivs[i+8];
        tcol[j] += pt[j] * derivs[i+16];
        }
      }

    for (unsigned int i=0; i<3; i++)
      {
      fcol[i] -= x[i];
      }

    //  compute determinants and generate improvements
    vnl_matrix_fixed<CoordRepType,3,PointDimension> mat;
    for(unsigned int i=0;i<PointDimension;i++)
      {
      mat.put(0,i,rcol[i]);
      mat.put(1,i,scol[i]);
      mat.put(2,i,tcol[i]);
     }

    d = vnl_determinant(mat);
    //d=vtkMath::Determinant3x3(rcol,scol,tcol);
    if ( vcl_abs(d) < 1.e-20)
      {
      return false;
      }

    vnl_matrix_fixed<CoordRepType,3,PointDimension> mat1;
    for(unsigned int i=0;i<PointDimension;i++)
      {
      mat1.put(0,i,fcol[i]);
      mat1.put(1,i,scol[i]);
      mat1.put(2,i,tcol[i]);
     }

    vnl_matrix_fixed<CoordRepType,3,PointDimension> mat2;
    for(unsigned int i=0;i<PointDimension;i++)
      {
      mat2.put(0,i,rcol[i]);
      mat2.put(1,i,fcol[i]);
      mat2.put(2,i,tcol[i]);
     }

    vnl_matrix_fixed<CoordRepType,3,PointDimension> mat3;
    for(unsigned int i=0;i<PointDimension;i++)
      {
      mat3.put(0,i,rcol[i]);
      mat3.put(1,i,scol[i]);
      mat3.put(2,i,fcol[i]);
     }

    pcoords[0] = params[0] - vnl_determinant(mat1) / d;
    pcoords[1] = params[1] - vnl_determinant(mat2) / d;
    pcoords[2] = params[2] - vnl_determinant(mat3) / d;

    if(pcoord)
      {
      pcoord[0] = pcoords[0];
      pcoord[1] = pcoords[1];
      pcoord[2] = pcoords[2];
      }

    //  check for convergence
    if ( ((vcl_abs(pcoords[0]-params[0])) < ITK_HEX_CONVERGED) &&
         ((vcl_abs(pcoords[1]-params[1])) < ITK_HEX_CONVERGED) &&
         ((vcl_abs(pcoords[2]-params[2])) < ITK_HEX_CONVERGED) )
      {
      converged = 1;
      }

    // Test for bad divergence (S.Hirschberg 11.12.2001)
    else if ((vcl_abs(pcoords[0]) > ITK_DIVERGED) ||
             (vcl_abs(pcoords[1]) > ITK_DIVERGED) ||
             (vcl_abs(pcoords[2]) > ITK_DIVERGED))
      {
      return -1;
      }

    //  if not converged, repeat
    else
      {
      params[0] = pcoords[0];
      params[1] = pcoords[1];
      params[2] = pcoords[2];
      }
    }

  //  if not converged, set the parametric coordinates to arbitrary values
  //  outside of element
  if ( !converged )
    {
    return false;
    }

  this->InterpolationFunctions(pcoords, weights);

  if(weight)
    {
    for(unsigned int i=0;i<8;i++)
      {
      weight[i] = weights[i];
      }
    }

  if ( pcoords[0] >= -0.001 && pcoords[0] <= 1.001 &&
  pcoords[1] >= -0.001 && pcoords[1] <= 1.001 &&
  pcoords[2] >= -0.001 && pcoords[2] <= 1.001 )
    {
    if (closestPoint)
      {
      closestPoint[0] = x[0]; closestPoint[1] = x[1]; closestPoint[2] = x[2];
      *dist2 = 0.0; //inside hexahedron
      }
    return true;
    }
  else
    {
    CoordRepType pc[3], w[8];
    if (closestPoint)
      {
      for (unsigned int i=0; i<3; i++) //only approximate, not really true for warped hexa
        {
        if (pcoords[i] < 0.0)
          {
          pc[i] = 0.0;
          }
        else if (pcoords[i] > 1.0)
          {
          pc[i] = 1.0;
          }
        else
          {
          pc[i] = pcoords[i];
          }
        }
      this->EvaluateLocation(subId, points, pc, closestPoint, (InterpolationWeightType *)w);

      *dist2 = 0;
      for(unsigned int i=0;i<3;i++)
        {
        *dist2 += (closestPoint[i]-x[i])*(closestPoint[i]-x[i]);
        }
      }
    return false;
    }
}

template <typename TCellInterface>
void
HexahedronCell< TCellInterface >
::InterpolationFunctions(CoordRepType pcoords[3], InterpolationWeightType sf[8])
{
  const double rm = 1. - pcoords[0];
  const double sm = 1. - pcoords[1];
  const double tm = 1. - pcoords[2];

  sf[0] = rm*sm*tm;
  sf[1] = pcoords[0]*sm*tm;
  sf[2] = pcoords[0]*pcoords[1]*tm;
  sf[3] = rm*pcoords[1]*tm;
  sf[4] = rm*sm*pcoords[2];
  sf[5] = pcoords[0]*sm*pcoords[2];
  sf[6] = pcoords[0]*pcoords[1]*pcoords[2];
  sf[7] = rm*pcoords[1]*pcoords[2];
}

template <typename TCellInterface>
void
HexahedronCell< TCellInterface >
::InterpolationDerivs(CoordRepType pcoords[3], CoordRepType derivs[24])
{
  const double rm = 1. - pcoords[0];
  const double sm = 1. - pcoords[1];
  const double tm = 1. - pcoords[2];

  // r-derivatives
  derivs[0] = -sm*tm;
  derivs[1] = sm*tm;
  derivs[2] = pcoords[1]*tm;
  derivs[3] = -pcoords[1]*tm;
  derivs[4] = -sm*pcoords[2];
  derivs[5] = sm*pcoords[2];
  derivs[6] = pcoords[1]*pcoords[2];
  derivs[7] = -pcoords[1]*pcoords[2];

  // s-derivatives
  derivs[8] = -rm*tm;
  derivs[9] = -pcoords[0]*tm;
  derivs[10] = pcoords[0]*tm;
  derivs[11] = rm*tm;
  derivs[12] = -rm*pcoords[2];
  derivs[13] = -pcoords[0]*pcoords[2];
  derivs[14] = pcoords[0]*pcoords[2];
  derivs[15] = rm*pcoords[2];

  // t-derivatives
  derivs[16] = -rm*sm;
  derivs[17] = -pcoords[0]*sm;
  derivs[18] = -pcoords[0]*pcoords[1];
  derivs[19] = -rm*pcoords[1];
  derivs[20] = rm*sm;
  derivs[21] = pcoords[0]*sm;
  derivs[22] = pcoords[0]*pcoords[1];
  derivs[23] = rm*pcoords[1];
}

template <typename TCellInterface>
void
HexahedronCell< TCellInterface >
::EvaluateLocation(int& itkNotUsed(subId),PointsContainer* points, CoordRepType pcoords[3],
                   CoordRepType x[3], InterpolationWeightType *weights)
{
  PointType pt;
  this->InterpolationFunctions(pcoords, weights);
  x[0] = x[1] = x[2] = 0.0;
  for (unsigned int i=0; i<8; i++)
    {
    pt = points->GetElement( m_PointIds[i] );

    for (unsigned int j=0; j<3; j++)
      {
      x[j] += pt[j] * weights[i];
      }
    }
}


} // end namespace itk

#endif